Paper supported by machine-verified Lean 4. The Harmonic Early-Warning Theorem (HEWT) recasts tipping-point monitoring as a thermodynamic detection problem and explains, from physics, a notorious failure of the ecological early-warning-signal (EWS) literature: spurious alarms exactly near the threshold. Its results: (i) a fluctuation–dissipation identity making the monitored variance equal to the system's susceptibility; (ii) a detection dissipation floor of 2 kB ln 2 per bit of early warning; (iii) the headline observability wall — the detection statistic peaks not at the threshold but at an interior optimal detection distance εₒpt=ε₀·3^ (−1/m), and the signal-to-noise ratio degrades as the threshold is approached (the physical origin of the spurious-alarm problem) ; (iv) a wu-wei active↔passive sensing crossover; and (v) detection efficiency equal to cos²Θ. This version (1. 0. 0) deposits the clean core (11 machine-verified theorems). Part of the S2 Monitoring series; derived from the Viridis Intelligence-Bound canon, concept DOI 10. 5281/zenodo. 19317982.
Hart et al. (Sun,) studied this question.